A numerical study is carried out to determine the linear optimal response of an axisymmetric premixed M-flame to periodic forcing. Direct numerical simulations are undertaken on the reactive Navier-Stokes equations. By solving these equations with selective frequency damping, we can obtain steady M-flame base flows about which our linear analysis is performed. The linear and adjoint operators are obtained by modular automatic differentiation of the full non-linear code. These operators enable us to find the optimal harmonic forcing and its corresponding output by performing a singular value decomposition on the resolvent. As each singular value decomposition is computationally expensive, we seek to extract a maximum amount of information from a single decomposition. Using a first-order accurate relation between the change in a singular value and a parametric change in the resolvent matrix, we easily and efficiently obtain sensitivities of the singular values with respect to forcing frequency and Reynolds numbers while avoiding additional singular value calculations. Using these tools, we carry out an input-output analysis for the response of an M-flame to harmonic forcing. Parametric sensitivities for the optimal gains are also determined for variations in the mean flow swirl, with special emphasis on frequency shifts for the optimal amplification rates.
|Original language||English (US)|
|Title of host publication||24th International Congress on Sound and Vibration, ICSV 2017|
|Publisher||International Institute of Acoustics and Vibration, IIAV|
|State||Published - Jan 1 2017|